Desmond Morris in Catwatching says that the cat is "performing it's highly specialised killing bite, as if it already had the unfortunate bird clamped between it's jaws".
The "killing bite" kills instantly, and it's import that the cat gets it right as if they misjudge, their prey can retaliate and hurt them. So they instinctively rehearse the move that they would make if they were catching the animal.
The noise is incidental, just something that happens when the cat makes that jaw movement.